[Nek5000-users] 2D simulation for 3D perturbation mode with a 2D baseflow

[nek5000-users at lists.mcs.anl.gov]

Hi Vincent,

Yes - this should be easy to implement.

For one thing, you have the option of inserting any forcing
in the rhs via ffx and ffy.

I've only glanced at the equations but am certain that they
can be inserted.

If it's an additional part that should be treated implicitly
in the Helmholtz solve there is a flag for that as well.  If
the multiplier is constant (w.r.t. space) then you can set
that term using param(107).

Paul


On Wed, 23 Oct 2013, nek5000-users at lists.mcs.anl.gov wrote:

> Hi Neks,
>
> I have a 2D baseflow and I am doing 3D perturbation mode calculation at a 
> prescribed spatial wavelength lambda=2pi/k (k the wavenumber) in the third 
> direction. The baseflow is assumed to be invariant in this third direction 
> therefore the perturbation can be chosen in the form u=uhat(x,y,t) e(ikz) 
> where z is the third direction and u=(u,v,w) and the baseflow is in the form 
> (U,V)(x,y) (in particular W=0).
>
> In this case the 3D linearized equations simplify to the following form
> duhat/dx+dvhat/dy+kwhat=0
> duhat/dt + U duhat/dx + V duhat/dy = -uhat dU/dx - vhat dU/dy + nu ( 
> d^2uhat/dxx+d^2uhat/dyy-k^2uhat )
> dvhat/dt + U dvhat/dx + V dvhat/dy = -uhat dV/dx - vhat dV/dy + nu ( 
> d^2vhat/dxx+d^2vhat/dyy-k^2vhat )
> dwhat/dt + U dwhat/dx + V dwhat/dy =  nu ( d^2what/dxx+d^2what/dyy-k^2what )
>
> I am currently doing 3D perturbation simulations with the box dimension in 
> the third dimension set to lambda but I was wondering if Nek offers the 
> possibility to run 2D simulations instead to solve for uhat(x,y,t).
>
> Indeed in the above equations, one does not need any mesh in the z direction. 
> A 2D mesh is enough but this means modifying slightly the linearized 
> equations to insert the k terms.
>
> I have been looking in the source files and I have found nothing like that so 
> I guess this is not currently in Nek.
> Any idea if that would be possible/easy to implement?
>
> Thanks a lot,
>
> Vincent.
>
>
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